{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PPR32G7JGGYF7TNTUGQNQD2556","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8eceebb1c9df08a2940b3120997e7cc6a98394ddcbf1241d77d25128c82c0b7b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-06-25T15:28:50Z","title_canon_sha256":"ea911e8b18b7632ff8db5508130970cbeb4eb0ab2a36ea8af8469f8e50284cc8"},"schema_version":"1.0","source":{"id":"1206.5709","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5709","created_at":"2026-05-18T03:52:39Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5709v1","created_at":"2026-05-18T03:52:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5709","created_at":"2026-05-18T03:52:39Z"},{"alias_kind":"pith_short_12","alias_value":"PPR32G7JGGYF","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PPR32G7JGGYF7TNT","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PPR32G7J","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:502acd36e1e9ad68de48d580860ae89328a0f9bfe7b3d209c365cb17e4b3cc9e","target":"graph","created_at":"2026-05-18T03:52:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The cryptographic protocol based on topological knot theory,recently proposed by the authors, is improved for what concerns the efficiency of the encoding of knot diagrams and its error robustness. The standard Dowker-Thistlethwaite code, based on the ordered assignment of two numbers to each crossing of a knot diagram and not unique for some classes of knots, is replaced by a system of eight prototiles (knot mosaics) which, once assembled according to a set of combinatorial rules, reproduces unambiguously any unoriented knot diagram. A Reed-Muller scheme is used to encode with redundancy the ","authors_text":"Annalisa Marzuoli, Giandomenico Palumbo","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-06-25T15:28:50Z","title":"Fault-tolerant mosaic encoding in knot-based cryptography"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5709","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9449cfa225ebae58927044f255b16d52eba6039004515033e2c188a91e0fb0ad","target":"record","created_at":"2026-05-18T03:52:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8eceebb1c9df08a2940b3120997e7cc6a98394ddcbf1241d77d25128c82c0b7b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-06-25T15:28:50Z","title_canon_sha256":"ea911e8b18b7632ff8db5508130970cbeb4eb0ab2a36ea8af8469f8e50284cc8"},"schema_version":"1.0","source":{"id":"1206.5709","kind":"arxiv","version":1}},"canonical_sha256":"7be3bd1be931b05fcdb3a1a0d80f5def9d052cdda5fdd2898b285f56725ea215","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7be3bd1be931b05fcdb3a1a0d80f5def9d052cdda5fdd2898b285f56725ea215","first_computed_at":"2026-05-18T03:52:39.279594Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:39.279594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J+xJiDvrtx/0++YMmDxeVKVVJA8UPt0gRVJ6q1MHaAPy5nJSdyw6hoV9F20mAQfMHi46p5VpRnqKjY4YB4EQBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:39.280171Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.5709","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9449cfa225ebae58927044f255b16d52eba6039004515033e2c188a91e0fb0ad","sha256:502acd36e1e9ad68de48d580860ae89328a0f9bfe7b3d209c365cb17e4b3cc9e"],"state_sha256":"c097357bd13d26a004c1063a696444de10e03827655d4ea771b2f04f901ad702"}